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Solve theses equations by elimination y= 3/2x -10 and -2x -4y =-8

Sagot :

SOLUTION

We want to solve the question with elimination method

[tex]\begin{gathered} y=\frac{3}{2}x-10.\text{ . . . . . . equation 1} \\ -2x-4y=-8\text{ . . . . . . . equation 2} \\ multiply\text{ equation 1 by 2, so as to remove the fraction } \\ 2\times y=(2\times\frac{3}{2}x)-(2\times10) \\ 2y=3x-20 \\ re-arranging\text{ we have } \\ -3x+2y=-20 \end{gathered}[/tex]

So our paired equation becomes

[tex]\begin{gathered} -3x+2y=-20 \\ -2x-4y=-8 \end{gathered}[/tex]

To eliminate y, multiply the upper equation by 4 and the lower by 2, we have

[tex]\begin{gathered} 4(-3x+2y=-20) \\ 2(-2x-4y=-8) \\ -12x+8y=-80 \\ -4x-8y=-16 \\ we\text{ have } \\ (-12x-4x)+(8y-8y)+(-80-16) \\ -16x+0=-96 \\ -16x=-96 \\ x=\frac{-96}{-16} \\ x=6 \end{gathered}[/tex]

So put x for 6 into the second equation, we have

[tex]\begin{gathered} -2x-4y=-8 \\ -2(6)-4y=-8 \\ -12-4y=-8 \\ -4y=-8+12 \\ -4y=4 \\ y=\frac{4}{-4} \\ y=-1 \end{gathered}[/tex]

Hence x = 6 and y = -1

The graph is shown below

Hence the point of intersection is (6, -1)

View image SophiagraceB628962
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